Question

0,25 elevado a x - 4 = a 0,5 elevado a - 2 x+1

Answer 1

0,25 elevado a x - 4 = a 0,5 elevado a - 2 x+1

0,25^x-4 = 0,5^-2x+1
(0,5^2)^x-4 = 0,5^-2x+1
2(x-4) = - 2x + 1
2x - 8 = -2x + 1
2x+2x = 8+1
4x= 9
x = 9/4

Answer 2

$(0,25)^{x-4} = (0,5)^{-2x+1} \\\\ (\frac{1}{4})^{x-4} = (\frac{1}{2})^{-2x+1} \\\\ (\frac{1}{2^{2}})^{x-4} = (\frac{1}{2})^{-2x+1} \\\\ (2^{-2})^{x-4} = (2^{-1})^{-2x+1} \\\\ \not 2^{-2x+8} = \not 2^{2x-1} \\\\ -2x+8 = 2x-1 \\\\ 4x = 9 \\\\ \boxed{x = \frac{9}{4}} \\\\\\ \boxed{\boxed{S = \{\frac{9}{4}\}}}$